Discrete analysis for single-pylon suspension bridges

This paper presents calculation methods, developed at Tallinn University of Technology (Idnurm 2004; Kulbach 2007), for the single-pylon suspension bridges stiffened by a girder. Classical suspension bridge consists of a geometrically non-linear cable, connected by hangers with an elastic linear stiffening girder, pylons in both ends of the bridge and anchor cables. Alternate form of a suspension bridge is a bridge, with only one pylon on the middle of the span and suspension cable is connected to the abutments or the ends of the stiffening girder. In the calculation of suspension bridges, the geometrically non-linear behaviour of the parabolic cable is the main problem. The linear methods of analysis suit only for small spans. A geometrically non-linear continual model is especially useful for classical loading cases – a uniformly distributed load on the whole or half span. But the modern traffic models consist of concentrated and uniformly distributed loads. The discrete model of a suspension bridge allows us to apply all kinds of loads, such as distributed or concentrated ones. The assumptions of the discrete method described here are: linear elastic strain-stress dependence of the material and absence of horizontal displacements of hangers. Hanger elongation is taken into account. Kabamojo tilto su vienu pilonu diskrečioji analizė Santrauka Straipsnyje pateikiamas skaičiavimo metodas, pasiūlytas Talino technikos universiteto mokslininkų (Idnurm 2004; Kulbach 2007) ir skirtas kabamųjų tiltų su vienu pilonu standumo sijai skaičiuoti. Klasikiniai kabamieji tiltai susideda iš geometriškai nietiesiško lyno, kuris tampriomis atotampomis sujungtas su standumo sija. Paprastai lynas būna pakabintas tarp dviejų pilonų, inkaruotų inkariniais lynais. Alternatyvi kabamųjų tiltų konstrukcija yra tokia, kai naudojamas tik vienas pilonas tilto viduryje, o pagrindinis geometriškai netiesiškas lynas yra inkaruojamas standumo sijos galuose. Skaičiuojant kabamuosius tiltus, pagrindinė problema yra parabolinio lyno geometrinio netiesiškumo elgsena. Tiesinė analizė tinkama tik mažiems tarpatramiams. Geometrinio netiesiškumo modelis ypač naudingas klasikinės apkrovos atveju – vienodai išskirstytai apkrovai visam arba pusei tarpatramio. Tačiau šiuolaikinius transporto modelius sudaro koncentruotos ir vienodai išskirstytos apkrovos. Diskretusis kabamojo tilto modelis leidžia mums taikyti visų tipų apkrovas, tokias kaip koncentruotos ir išskirstytos. Diskrečiojo modelio prielaidos yra tokios: taikoma medžiagų ir horizontalių atotampų poslinkių tiesinė įtempių ir deformacijų priklausomybė. Atotampų pailgėjimas taip pat yra įvertintas. First Published Online: 16 May 2013 Reikšminiai žodžiai: lynų konstrukcijos, standumo sijos, kabamasis lynas, didelių tarpatramių konstrukcijos, diskrečioji analizė, geometrinis netiesiškuma

Life cycle analysis of reinforced concrete bridges in Baltic countries

During this paper the first part of Life Cycle Analysis based on visual inspection data of main types of reinforced concrete bridges in Baltic countries will be introduced and discussed. In a first step, the background of bridge management systems, visual inspections and most common bridges will be presented. During this step, an explanation of differences and similarities of Baltics visual inspections and data processing will be introduced. In a second step, principal component analysis with main outcomes for different Baltic countries and possible reasons for those outcomes will be discussed. Also a comparison of principal components for similar bridges in all Baltic countries will be shown. At the end, input for predictive models will be introduced. The main objective of this input is to show what elements deteriorate more rapidly and due to that have an influence for Life Cycle of reinforced concrete bridgesThe authors would like to gratefully acknowledge supporting of TU1406 – Quality specifications for roadway bridges, standardization at a European level (BridgeSpec), a COST Action supported by EU Framework Programme Horizon 2020.info:eu-repo/semantics/publishedVersio

RC bridge management optimisation considering condition assessment uncertainties

Decision-making in bridge management has changed considerably in the past two decades and owners are additionally considering what types of interventions to implement, but correct decisions still need certain input. In Estonia, like in many countries, bridge management is based on inventory records and condition information. The main emphasis of this investigation is on improving the regular condition assessment. More accurate nondestructive testing methods and optimised inspection scheduling are proposed, to reduce condition assessment uncertainties. A conversion matrix for translating additional assessment results to the rating scale of the current Estonian Transport Administration management system is introduced and uncertainties in the condition state are analysed probabilistically. In addition, stochastic degradation models based on existing information are investigated to help considering uncertainties as a part of the overall management process. What impact the adopting of quantitative assessment, rather than qualitative visual inspection, may have on the suggested interventions schedule is also analysed. The probabilistic characteristics of the condition profiles of the most common bridge elements are computed using Markov Chain Monte Carlo stochastic simulation. The optimisation of inspection scheduling is performed considering the uncertainty of the initial deterioration model. When a threshold value, defined by the owner, is reached, the model is updated with assessment data to maintain the level of uncertainty below that threshold. The results confirm that deviations in the degradation model and assessment results influence the bridge condition uncertainty. Likewise, times of both inspection and intervention are influenced, which will ultimately impact the overall management reliability and costs.The authors acknowledge the support of Eurostruct endorsed by the EU Framework Program Horizon 2020, the Archimedes Foundation and Professor Karl Oiger Scholarship Foundation. The publication costs of this article were covered by the Estonian Academy of Sciences

Non‐linear analysis of suspension bridges with flexible and rigid cables

One of the main problems related to the design of suspension bridges is stabilisation of their initial form. The tendency of suspension bridges to deform is generally determined by the kinematical displacements of the suspension cable caused by asymmetrical loads rather than by the elastic deformations. There are some suspension bridges when the so‐called rigid (stiff in bending) cables instead of usual flexible cables are suggested for stabilisation of their initial form. The analysis methods of such suspension bridges with rigid cables are underdeveloped. For the analysis of classical suspension bridges analytical models can be applied. However, in case of concentrated forces, the numerical techniques are preferred. The article presents analytical expressions for the calculation of internal forces and displacements of suspension bridges with a rigid cable. The article also discusses the discrete calculation model for classical suspension bridges. Santrauka Viena iš pagrindiniu kabamuju tiltu projektavimo problemu yra pradinus ju formos stabilizavimas. Kabamuju tiltu deformatyvuma lemia iš esmes ne tiek tampriosios deformacijos, kiek asimetriniu apkrovu sukelti kinematiniai kabamojo lyno poslinkiai. Yra žinomi kabamieji tiltai, kuriu pradinei formai stabilizuoti siūloma vietoje iprastiniu lanksčiuju lynu taikyti vadinamuosius standžius lynus. Tokiu kabamuju tiltu su standžiaislynais skaičiavimo metodai nera iki galo parengti. Klasikiniams tiltams su lanksčiu lynu skaičiuoti taikomi daugiausia kontinualūs modeliai, kurie esant tam tikrai tilto sandarai ar veikiant sutelktoms apkrovoms nera pakankamai tikslūs. Straipsnyje pateikiamos analizines išraiškos kabamuju tiltu su standžiu lynu iražoms ir poslinkiams apskaičiuoti, aptariamas diskretusis klasikiniu kabamuju tiltu skaičiavimo modelis. Published Published Online: 24 Jun 2011 Reikšminiai žodžiai: kabamasis tiltas, lankstus lynas, standus lynas, netiesine analize, kontinualus ir diskretinis modeliai, iražos ir poslinkiai

Statistical analysis of reinforced concrete bridges in Estonia

This paper introduces a possible way to use a multivariate methodology, called principal component analysis, to reduce the dimensionality of condition state database of bridge elements, collected during visual inspections. Attention is paid to the condition assessment of bridges in Estonian national roads and collected data, which plays an important role in the selection of correct statistical technique and obtaining reliable results. Additionally, detailed overview of typical road bridges and examples of collected information is provided. Statistical analysis is carried out by most natural reinforced concrete bridges in Estonia and comparison is made among different typologies. The introduced multivariate technique algorithms are presented and collated in two different formulations, with contrast on unevenness in variables and taking into account the missing data. Principal components and weighing factors, which are calculated for bridges with different typology, also have differences in results and element groups where variation is retainedTU1406 – Quality Specifications for Roadway Bridges, standardiza- tion at a European level (BridgeSpec), a COST Action sup- ported by EU Framework Programme Horizon 2020info:eu-repo/semantics/publishedVersio

Discrete Analysis Method for Suspension Bridges

In the calculation of suspension bridges, the geometrically non-linear behaviour of the parabolic cable is the main problem. The linear methods of analysis suit only for small spans. A geometrically non-linear continual model is especially useful for classical loading cases - a uniformly distributed load on the whole or a half span. But the modern traffic models consist of concentrated and uniformly distributed loads. The discrete model of a suspension bridge allows us to apply all kinds of loads, such as distributed or concentrated ones. The simplest suspension bridge consists of a geometrically non- linear cable, connected by hangers with an elastic linear stiffening girder. Depending on the load case, the hangers may be unequally loaded; thus the cable may also be loaded by unequal concentrated forces. The assumptions of the discrete method described here are: linear elastic strain-stress dependence on the material and absence of horizontal displacements of hangers. Hangers elongation is taken into account. Some comparative numerical examples are presented

Discrete Analysis of Elastic Cables

This paper presents a discrete calculation method for an elastic cable loaded by static concentrated forces. The discrete method is suitable to use for all suspension structures (bridges, roofs). In the calculation of the elastic cable the main problem is the geometrically non-linear behaviour of the parabolic cable. The linear methods of analysis are suitable only for small spans. A geometrically non-linear continual model is especially useful for classical loading types, e.g. uniformly distributed loads. The discrete model of suspension structures allows applying all kinds of loads, such as distributed or concentrated ones. The assumptions of the discrete method described here are: the stress-strain dependence of the material is linear, the area of the cross-section of the cable is unchangeable during the elongation and the flexural rigidity of the cable is not taken into account. An experimental investigation was conducted to prove this calculation method

Kabamųjų tiltų su lanksčiu ir standžiu lynais netiesinis skaičiavimas

One of the main problems related to the design of suspension bridges is stabilisation of their initial form. The tendency of suspension bridges to deform is generally determined by the kinematical displacements of the suspension cable caused by asymmetrical loads rather than by the elastic deformations. There are some suspension bridges when the so-called rigid (stiff in bending) cables instead of usual flexible cables are suggested for stabilisation of their initial form. The analysis methods of such suspension bridges with rigid cables are underdeveloped. For the analysis of classical suspension bridges analytical models can be applied. However, in case of concentrated forces, the numerical techniques are preferred. The article presents analytical expressions for the calculation of internal forces and displacements of suspension bridges with a rigid cable. The article also discusses the discrete calculation model for classical suspension bridges.Lietuviška santrauka. Viena iš pagrindinių kabamųjų tiltų projektavimo problemų yra pradinės jų formos stabilizavimas. Kabamųjų tiltų deformatyvumą lemia iš esmės ne tiek tampriosios deformacijos, kiek asimetrinių apkrovų sukelti kinematiniai kabamojo lyno poslinkiai. Yra žinomi kabamieji tiltai, kurių pradinei formai stabilizuoti siūloma vietoje įprastinių lanksčiųjų lynų taikyti vadinamuosius standžius lynus. Tokių kabamųjų tiltų su standžiais lynais skaičiavimo metodai nėra iki galo parengti. Klasikiniams tiltams su lanksčiu lynu skaičiuoti taikomi daugiausia kontinualūs modeliai, kurie esant tam tikrai tilto sandarai ar veikiant sutelktoms apkrovoms nėra pakankamai tikslūs. Straipsnyje pateikiamos analizinės išraiškos kabamųjų tiltų su standžiu lynu įrąžoms ir poslinkiams apskaičiuoti, aptariamas diskretusis klasikinių kabamųjų tiltų skaičiavimo modelis

Uncertainty in condition prediction of bridges based on assessment method – Case study in Estonia

In this paper the uncertainty in condition assessment based on most common assessment methods, visual inspection and non-destructive testing, is investigated. For decision-making the averaged or estimated value is suitable, but if the basis of a decision is only a subjective visual inspection, then it could lead to a wrong decision. The second most traditional assessment method is non-destructive testing (NDT), which can give reliable results, but the interpretation of measurement is needed. To investigate the errors in both evaluations, benchmarking tests were carried out in Estonia within two groups, a group of experienced inspectors and a group of unexperienced students, to show how the importance of experience affects results. To present the influence of assessment uncertainty to condition prediction curves based on continuous-time Markov model are calculated and for updating, Bayesian inference procedure is used.- (undefined

Geodetic Monitoring of Bridge Deformations Occurring During Static Load Testing

Terrestrial laser scanning technology has developed rapidly in recent years and has been used in various applications but mainly in the surveying of different buildings and historical monuments. The use for terrestrial laser scanning data for deformation monitoring has earlier been tested although conventional surveying technologies are still more preferred. Since terrestrial laser scanners are capable of acquiring a large amount of highly detailed geometrical data from a surface it is of interest to study the metrological advantages of the terrestrial laser scanning technology for deformation monitoring of structures. The main intention of this study is to test the applicability of terrestrial laser scanning technology for determining range and spatial distribution of deformations during bridge load tests. The study presents results of deformation monitoring proceeded during a unique bridge load test. A special monitoring method-ology was developed and applied at a static load test of a reinforced concrete cantilever bridge built in 1953. Static loads with the max force of up to 1961 kN (200 t) were applied onto an area of 12 m² in the central part of one of the main beams; the collapse of the bridge was expected due to such an extreme load. Although the study identified occurrence of many cracks in the main beams and significant vertical deformations, both deflection (–4.2 cm) and rising (+2.5 cm), the bridge did not collapse. The terrestrial laser scanning monitoring results were verified by high-precision levelling. The study results confirmed that the TLS accuracy can reach ±2.8 mm at 95% confidence level